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ARLINGTON, Texas (WFAN/AP) — Immediately after the Red Sox landed Carl Crawford, the Yankees boosted their already whopping offer to Cliff Lee. Their high-stakes rivalry is escalating, hundreds of millions of dollars by the hour.

Not everyone is out of the mix, though.

Texas Rangers owner Chuck Greenberg traveled to Arkansas on Thursday and presented Lee with a “menu of multiple offers” in an attempt to persuade the prized pitcher to remain with the team he helped reach the World Series.

While Greenberg would not get into specific details, he said Thursday night the offers included “substantial additional commitments in years and dollars.” He characterized them as “highly competitive.”

The Yankees added a year to their offer Thursday, proposing a seven-year contract for the 2008 AL Cy Young Award winner. On Wednesday, the Yankees offered a six-year deal worth $137.5 million to $140 million.

The Yankees may have to sweeten their offer even further to land the coveted left-hander.

“He is worth waiting for,” GM Brian Cashman said Thursday. “You have to let the process play out and ultimately respect his decision.”

Before Thursday, the Rangers had asked Lee to tell them what it would take for him to stay with Texas, which acquired the ace left-hander from Seattle in July.

Asked if he considered himself optimistic or pessimistic about that happening after the nearly 90-minute meeting, Greenberg responded, “We felt very good about the discussion.”

Greenberg, whose group bought the team from Tom Hicks in August, said the Rangers weren’t given a timetable for Lee’s decision. And they didn’t push for one either since a “considerable amount” of new information was presented to the pitcher and his family.

“We’d rather it be sooner than later,” the owner said, “but they have an enormous decision to make.”

It was the third time Rangers officials visited Lee in his home state. Team president Nolan Ryan and general manager Jon Daniels were involved in the earlier trips, and Greenberg also visited previously.

The 32-year-old Lee was a combined 12-9 with a 3.18 ERA for Seattle and Texas last season. He was 7-0 with a 1.26 ERA in eight career postseason starts before twice losing to San Francisco in the World Series.

Greenberg said the new ownership group’s commitment to having a championship-level team was reaffirmed to Lee, who has said he enjoyed his short time in Texas.

Greenberg also said the Rangers wouldn’t be limited or at a financial disadvantage to put together a competitive roster if Lee does sign.